Theorem

Many inside-outs (inverts) bounce off the receivers hands and into their chests because they don't adjust their catch to the unexpected reverse spin of the disc.If you have ever played on a "mac" line, you will have realized that there is a correct side to mac the disc on, as well as an incorrect side (which stops the disc dead). The perfect catch is the opposite of the perfect mac.

There is a firm physical basis for doing this and it relates to the parallel axis theorem.

This theorem (actually a related theorem) states that the total angular momentum of the disc (about the receiver's hand) is the vector sum of two components;

1. The angular momentum of the disc about its own center of mass (rotational),

2. The component due to the disc's translational movement with respect to your hand.

If you catch the disc in the appropriate position along its rim, these two components will cancel each other (yielding zero net angular momentum) and the center of mass of the disc will push itself directly into the palm of your hand.

OBVIOUSLY, If can grab the disc firmly, just grab it and the disc won't go anywhere (two hands, pancake, etc).

The method described here is only for very specific situations (when you can only get one hand on a fast moving, hard to catch disc) and is simply another tool to use.

The following derivation is used to indicate where this position is on the rim of the disc (by the way, you don't have to calculate these equations every time you catch it).

This will be hard without a visual, but here goes,

If the disc is traveling directly towards you (the receiver), label the point on the rim of the disc closest to yourself as theta = 0 degs. Angles to the right (viewed by yourself) are labeled positive angles, left indicates negative.

If the disc is traveling with velocity V (with respect to you) and spin w (lefty forehand, righty backhand), the disc will have angular momentum (about your hand) resulting from two components; rotational and translational;

L = Lrotational + Ltranslational

These components are vectorially summed to yield the total angular momentum;

where;

I = moment of inertia of the disc
w = angular velocity of the disc
z = unit vector in the z hat direction pointing
vertically upwards (couldn't find a hat)
R = Radius vector from your initial point of contact to
the center of the disc
m = mass of the disc
V = Velocity vector of the disc
v = velocity of the disc (magnitude)
r = radius of the disc
theta = angle between the centerline of the disc's path and
the point of contact by the receiver
x indicates the vector cross product

To determine the moment of inertia I of the disc; realize that for a perfectly flat disc with a uniform mass distribution, I is equal to;

For a perfect hoop with all of the mass concentrated at the rim, I is equal to;

So, we can approximate the momentum of inertia of a Discraft ultra-star as being somewhere in-between these two;

If we take a "typical" forehand as being that which would roll along the floor without slipping (if thrown sideways) we obtain;

Plugging these into above; we obtain;

Now, if we choose an angle where the total angular momentum (about your hand) is zero, then the disc will not try to rip itself out of your hand as you grab it.

Setting L equal to zero;

L = 0

we get;

or;